I observed that many epubs checked by epubchecker isn't valid because there are a lot of errors produced by this tool. But the epubs can be viewed without problems on my readers. So the question arise, whether the correctness of an epub according to the standard is important.

Correct ePubs are better because you can trust more on the presentation of the content. Incorrect ePubs are always interpreting on what the author could have meant and may vary from ereader to ereader or more worse from firmware to firmware on the same reader.

1. Do producers of ereaders really implement their firmwares in such a manner that epubs conforming to the standards are surely displayed correct?

2. If I test some ebooks from shops that sell them without DRM epubcheck also issued a lot of errors. So there is the question, how many epubs commercially sold are really formated according to the standards. (So that we will be able to read them using firmwares developed in 5 years ;-) )

What standards? Many companies add their own bells and whistles to the format, which might then be seen as errors by the validators. Hopefully those are made in a way that don't cause harm to readers. So the errors might not be important.

Also, just because an epub is valid does not mean it's error free; there's still typos and formatting errors in them. The series I'm currently reading is like that (Skulduggery Pleasant, bought from Amazon because the epub shoppes refuse to sell outside UK/US).

Fixing those content related issues is more important than insisting on standards, although it'd naturally be best to have both.

I always try to have them error free and succeeded in that so far. That does not guarantee, unfortunately, that all readers display them as I want. However, that is because the readers don't honor the ePUB specifications.
If the ePUB contains errors, it is much more a hit and miss if the ePUB is rendered correctly. It might, but that is only because the reader is willing to correct errors which should not be there in the first place.

It all depends on the actual errors. There might be structural errors (which I feel must be corrected), files in the ePUB which are not used (easy to solve, gives bloat in the file), wrong references (mostly annoying) or new stuff which might be correct according to ePUB3 but not in the checktools yet.

1. Do producers of ereaders really implement their firmwares in such a manner that epubs conforming to the standards are surely displayed correct?

Since there are e-books on the market which don't met the standard (see your No. 2 ), firmware developers won't risk that those books can't be displayed on their readers. It would make their readers less favourable to the customer.

Quote:

Originally Posted by comet

2. If I test some ebooks from shops that sell them without DRM epubcheck also issued a lot of errors. So there is the question, how many epubs commercially sold are really formated according to the standards. (So that we will be able to read them using firmwares developed in 5 years ;-) )

How should we know ? In most cases, we can't check. But if i see a "professional made" EPUB with an undistorted cover-image, i guess, the rest of the thing would never pass an epubcheck. The same is if there are too much typos...

Look around in the forums here ! A few days ago i stumbled over some queries from an epub-maker. From his questions i could see that he uses some kind of software to produce the book and his sole problem was the checking-software of the dealer. Finally he managed to pass the test somehow (I guess with some help frome here). You may buy the book by now for 6.95 EUR.